Sampling Procedures for Extending the Use of
the Fishbone Diagram
Frank J. Matejcik
Industrial Engineering
South Dakota School of Mines and Technology
501 E. St. Joseph Street, Rapid City, SD 57701 -3901
Phone (605) 394-6066 e-mail: Frank.Matejcik@sdsmt.edu
http://webpages.sdsmt.edu/~fmatejci/EIPI/EIPIhome.html
Keywords: Fishbone; Ishikawa; capture; recapture
ABSTRACT
Procedures for creating a Fishbone diagram often assume all the possible participants are available.
However, sampling among the participants may be required. The sampling problem is similar to a capture
recapture. Methods for sampling decisions and experiences from classroom trials are discussed. Potential
applications are mentioned, also.
I INTRODUCTION
The paper begins in the following section with a background
discussion of how Ishikawa diagrams are currently used. The
following section discuss the need for extending the method and
the quality circle basic tool for gathering data to extend the
method, which results in providing data as if we have a capturerecapture experiment. Accordingly, the fourth section discusses
the state of the art of capture-recapture methods. Section five
discusses how our problem is different than ecological
experiments, which leads to section six that gives the details of a
general procedure for applying the extended method. A
relatively simple method computing estimates of completeness
and suggestion follow up sample sizes is given in section seven.
The question of how an Ishikawa diagram may formally lead to
further study is considered when section eight presents a
complimentary procedure, a Pareto diagram related question set.
Section nine discusses my current work. The article concludes
with a summary section.
II ISHIKAWA DIAGRAM CURRENT
STATE
The Ishikawa Diagram is also referred to as a fishbone diagram
or a cause and effect diagram. Cause and effect describes the
elements of the diagram. The diagram is begun by considering
the effect, which may be a quality problem in a factory, a desired
characteristic in an education system, or any clearly described
condition. The diagram is drawn by applying a network of
contributing causes. The completed network diagram (as show in
figure 1) resembles a fishbone, in which the contributing causes
branch from a main spine. Note that the sample graphics
provided have fewer details than are typical in common use.
Figure 1 generic Ishikawa diagram
Figure 1 was prepared using Microsoft Visio, which is a chart
tool which can be integrated with Microsoft Office. Visio has a
special file request for the Cause and Effect diagrams. Of course,
a Visio file can be e-mailed and used by all users with Visio. It
can save to formats that can be read more generally. Visio has a
free software/open source competitor Dia. There is no special
file request for the Ishikawa diagram in Dia, but with the more
general tools in Dia an Ishikawa diagram can be prepared. The
format of the Dia file is open and can be used by other programs
for further manipulations. The Draw tool in Open Office can
also be used to create Ishikawa diagrams, and the format is of
course open. The drawing tools in Microsoft Word can also be
used to prepare an Ishikawa diagram. Pencil and paper can be
used to create diagrams, and they can be readily scanned as a
graphics file and e-mailed.
The Ishikawa diagram is part of the Quality Circle training that
was developed in the 1960’s in Japan. All of these tools have
been taught broadly and successfully since the 1960’s.
Accordingly, many people are familiar with the method and
teaching resources for the method are abundant. So, there is not
reason to prevent the further teaching of the method.
The Ishikawa diagram is discussed beyond the Quality
community. Some researchers have listed it among Qualitative
Research tools. It is a competitor to other general qualitative
research tools, such as focus groups. Much of my work here is
inspired by a colleague’s suggestion that an Ishikawa diagram
can be constructed to analyze a focus group transcript. My
immediate response was “Why not just do an Ishikawa
diagram?”
procedure can get quite detailed considering combining takes
some work, sampling decisions are involved in the process,
allowance for noting disagreement should be possible, and
record keeping to aid the sampling needs to be done.
For record keeping we use a check sheet, another Quality Circle
tool. Each cause on the Ishikawa diagram is listed vertically on
the check sheet, and each individual involved being listed
horizontally. See figure 2 for a generic example of a check sheet.
Many sources (e.g. Ishikawa (1986), Juran and Godfrey (1998))
describe the Ishikawa diagram, but do not describe the procedure
for getting the ideas from people’s minds to a diagram. Swanson
(1995) does describe the process as beginning with a
brainstorming session and continuing much like a brainstorming
meeting. The drawing is constructed as a brainstorming notes
record. Swanson (1995) mentions that frequently voting is done
with the group, and the group making a recommendation of
action for improving the situation described by the effect.
There are some implicit assumptions with this method. To run a
brain storming session under conventional technology, everyone
has to be in the same room. With additional technological
enhancements everyone has to be working at the same time.
Another assumption is that there enough people to state the
causes that will help remedy the problem most effectively. There
is a question that the people constructing the diagram have broad
enough backgrounds to complete the task. Lastly, there is an
assumption that there is no formal rule for deciding that the
diagram is complete.
In the next section we describe procedures that extend the use
the Ishikawa diagram both for situations where the people
involved are at multiple sites and where sampling is required.
The organization and additional documents required to deal with
sampling also makes multiple site problems tractable.
Fortunately, the use of e-mail makes transferring partially
completed Ishikawa diagrams a relatively easy task, and by its
nature e-mail is asynchronous.
III APPLYING CAPTURE-RECAPTURE
METHODS
In an overview, we assign individuals to complete Ishikawa
diagrams and then the individual diagrams are combined.
Combining the diagrams requires some discussion, because
different terms may be used for the same object. Also, we have
found from our trials with freshmen and work study students at
the South Dakota School of Mines and Technology (SDSM&T)
that having individuals begin with a common set of categories
(see figure 1) for the Ishikawa diagram makes the task easier.
We have not yet tried the procedure in a multi-site situation. The
Figure 2 a generic check sheet
The data in this form has the same patterns as the results of
animal abundance studies using capture- recapture methods. The
causes in the extended Ishikawa procedure replace animals in
animal abundance studies, and individuals in the extended
Ishikawa procedure replace trapping sessions in animal
abundance studies.
IV STATE OF THE ART OF CAPTURERECAPTURE METHODS
Capture-recapture methods are a mature area of Statistics with a
long history. A particularly accessible recent book is Amstrup
(2005). Additionally, the research is ongoing; Royle et al (2007)
is a recent article describing Markov Chain Monte Carlo
procedures for capture-recapture methods using WinBUGS.
Anne Chao’s website ( http://chao.stat.nthu.edu.tw/indexE.html )
includes numerous reference articles and software for
performing Capture-Recapture analysis. An extensive computer
package with a 600 page free *.pdf file is MARK, which is
available for free at
http://www.warnercnr.colostate.edu/~gwhite/mark/mark.htm
. Much of the best software in capture-recapture methods has
been developed by government organizations and is available for
free.
Royle et al (2007) describes other applications for capturerecapture methods. Most notably in software testing, where an
error plays the role of animal, and tester replaces a capture
session. Our application is similar in the sense that people
replace capture sessions and observations replace the animals.
V DIFFERENCES IN OUR QUESTION
Many of the models for capture-recapture studies involve
continuous time sampling, which is not applicable in our setting.
In fact, all trapping session are done at different times, whereas
many Ishikawa diagrams are done at the same time.
Additionally, the population of humans that may be sampled is
finite. For example, we may be seeking opinions from students
at one school or from workers for one company. This gives a
finite sampling concern that does appear in ecological studies.
Also, the causes in an Ishikawa diagram have a hierarchical
nature, which animals do not have.
VI EXTENDED ISHIKAWA PROCEDURE
The procedure has a few layers. Stages contain steps; rounds are
repeated sequences of steps. We work from the effect to a
verified completed Ishikawa diagram.
Preliminary Setup
Phrase an effect statement to be studied. Select a team
to begin the first chart, and manage the process. The
team should represent the diversity of the entire
population, and be at least five members to allow all
common statistics to be computed. Our experience
indicates that groups of nine or larger work more
slowly.
Stage 0 Category Selection
Step 0.0 each team member is asked to write a list of
categories.
Step 0.1 the team creates a combined list of the
categories written in Step 0.0.
Step 0.2 additional categories may be suggested by
team members and added to the list created in Step 0.1.
Step 0.3 the team decides which categories will be
included on the Ishikawa diagram. If a large number of
categories are suggested for one diagram, multiple
Ishikawa diagrams could be used with new effect
statements that partition the original effect statement.
Each of the multiple Ishikawa diagrams must follow the
rest of the procedure separately.
Stage 1 Diagram Initiation
Step 1.0 team selects the locations of the categories on
the Ishikawa diagram.
Step 1.1 each team member completes an individual
Ishikawa diagram. A team member may add additional
categories on the individual Ishikawa diagram at this
time, if inspired by the work of constructing the
diagram.
Step 1.2 the team members prepare a composite
Ishikawa diagram based on Step 1.1 alone.
Step 1.3 each cause on the composite diagram should
be labeled with a number. Label the corresponding
causes on the individual Ishikawa diagrams. This step
helps insure each item from the individual diagram is
included on the composite diagram.
Step 1.4 the team members prepare a check sheet based
on Steps 1.1-1.3 alone. Include labels from Step 1.3 on
the check sheet causes also.
Step 1.5 since viewing the work of others may inspire
team members to observe additional causes (and
possibly categories), team members may prepare an
additions sheet which contains the new causes and/or
categories.
Step 1.6 team members update the composite Ishikawa
diagram from information on the additions sheets.
Step 1.7 team members update the Check Sheet from
information on the additions sheets.
Step 1.8 Add label numbers to the revised diagram, the
check sheets and the additions sheet analogous to Step
1.3
Repeat Steps 1.5 through 1.8 more as many rounds as
required by the team.
Step 1.9 Compute Statistics from the Check Sheets if
sampling is to be done. The next section describes
procedures for these calculations.
Step 1.10 Determine whether a completion group is
needed. If the group is not needed, go to Stage 3. If
needed go to Step 1.9.
Step 1.11 Compute an additional sample size for a
completion group. The next section describes
procedures for these calculations. Sometimes for
convenience or political concerns all possible people
may be included in the completion group. Go to Stage 2
Stage 2 Diagram completion
Step 2.1 Select a completion group.
Step 2.2 Send each member of the completion group a
copy of the currently updated Ishikawa and request that
the additions be sent to the team.
Step 2.3 completion group makes additions (causes and
possibly categories) and sends the results to the team.
Step 2.4 the team members prepare an updated
Ishikawa diagram based on Step 2.3 alone.
Step 2.5 the team members prepare a Check Sheet
based on Step 2.3 alone.
Step 2.6 Add label numbers to the revised diagram, the
check sheets and the additions sheet analogous to Step
1.3
Step 2.7 since viewing the work of others may inspire
team members to observe additional causes (or possibly
categories), team members now send updated Ishikawa
diagrams to the group.
Step 2.8 group members may prepare an additions sheet
which contains the new causes (or possibly categories),
and return them to the team.
Step 2.9 team members update the composite Ishikawa
diagram from information on the additions sheets.
Step 2.10 team members update the Check Sheet from
information on the additions sheets.
Step 2.11 Add label numbers to the revised diagram,
the check sheets and the additions sheet analogous to
Step 1.3
Repeat Steps 2.7 through 2.11 for as many rounds as
required by the team.
Step 2.12 Compute Statistics from the Check Sheet
began at Step 2.5. The next section describes
procedures for these calculations.
Step 2.13 Determine whether an additional completion
group is needed. If the group is not needed, go to Stage
3. If needed go to Step 2.14.
Step 2.14 Compute an additional sample size for a
completion group and go to Step 2.1. The next section
describes procedures for these calculations.
Stage 3 Follow Up Study
Stage 4 Reporting
Estimates of sample size and checks of completeness are
introduced in the next section. A recommended follow up
activity is included in section VIII. Reporting depends on the
follow up training, the audience, and the team.
VII A COMPLETION CHECK RULE AND
A COMPLETION SAMPLE SIZE
ESTIMATE
We choose our notation to generally be consistent with Amstrup
et al (2005). Let
Mk+1 = the number of causes found on the latest check sheet
MTOT = the total number of causes found since the end of stage 0.
N̂ = Estimated number of causes including only Mk+l, and the
currently unobserved.
̂ standard error of N̂
B̂ = Nˆ  M k 1

 ˆ 2  


C = exp 1.96 ln 1  2   from page 66,

 Bˆ  


Amstrup et al (2005)
d = portion of causes not observed
Bˆ
D̂ =
an estimate of d
Bˆ  M TOT
k = the number of users that have contributed to the most recent
check sheet
p = the assumed probability of a cause being observed by an
individual in the next check sheet
q=1−p
r = the number required number causes to be observed so that d
will be as small as desired.
INT = an intermediate term, the mean of the geometric
distribution order statistic based on r and p
2
 = an intermediate term, the second moment of the
E X INT
geometric distribution order statistic based r and p
k+ = the number of users that we select to contribute to the next
set of additions and be part of the next check sheet
To check the completion of the Ishikawa diagram begin by
observing Mk+l and MTOT from the most recent check sheet data.
Estimate N̂ and ̂ from the check sheet and calculations,
which may be done using CARE-2 or another package. CARE-2
is easy to use, and computes many estimates of N̂ , ̂ and the
Akaike Information Criteria. Judge appropriate values for both
terms. Compute a point estimate of d, D̂ . Also, a 95%
confidence interval for d is


Bˆ
CBˆ


,
 CM  Bˆ M
ˆ

C
B
TOT
TOT


N̂ is given, an interval
If an interval estimate (NLB, NUB) for
estimate of d, is


N LB  M k 1
NUB  M k 1

 .
,
 N LB  M TOT  M k 1 NUB  M TOT  M k 1 
If both the point and interval estimates of d are as small as
desired, no additional groups need be sampled.
Future work will likely use simulated check sheet data to decide
an appropriate number of people to be selected for an additional
group, k+ . Here we use formulas based on approximate moments
of the order statistics for the geometric distribution, which are
listed in Evans et al (2006).
Select a value for p. You may choose the median probability of a
1
cause in the previous check sheet p  1  0.5 k . You may
choose the average probability of a user selecting a cause from
the previous check sheet p 
n
i
k  M k 1
. Other reasonable
choices exist.
Choose a desired level of d, and then find the smallest integer r
ˆ r
such that B
1  d Bˆ  d MTOT .
Finally, use the following three formulas to compute k+.
INT
 r  1
( 1) j 

r

1
ˆ  1

j
B



 Bˆ 
Bˆ  r  j 1

ˆ
)
 r  1  j  0 ( B  r  j  1)(1  q
 r  1
ˆ
( 1) j 
(1  q B  r  j 1 )
ˆ
2
  Bˆ  B  1 ˆ  j 
E X INT
Bˆ  r  j 1
)
 r  1  j  0 ( B  r  j  1)(1  q
r 1
2
 INT 
k    INT  2 E X INT
this is revolutionary. A qualitative tool is simple and cheap. A
qualitative tool uses formal sampling and includes estimates of
completeness. The quantitative tool is simple to prepare and
leads to short, direct reports. In some cases (e.g. classroom
assessment and workplace multi-site problems with small
populations) EIPI can be used with the completion group and the
Pareto question group being the entire population, which
simplifies the entire procedure to a Quality Circle level. Future
work may lead to more convenient methods for estimating d and
k+ , so most EIPI analyses to be performed at a Quality Circle
level.
2
VIII EIPI
Once our work on the Ishikawa diagram (and possibly the check
sheet) is completed, then we have a list of possible causes.
Conventional quantitative analysis would lead to a survey with
many questions. Our simplification is asking a few questions
about the entire list of causes. Questions of this form include,
“Which one cause is most important?”, “If you were to spend
$10,000 to improve the situation, how much would you spend on
each cause?”, and “Where on a scale of 1 to 6 would you rate
each of the causes with 6 being the most important?”. The
answers to our questions about the Ishikawa diagram causes can
be summarized in a Pareto chart (shown in figure 3 below) (see
e.g. Ishikawa (1986) or Juran and Godfrey (1998)). Pareto charts
give direction for addressing problems. Hopefully, writing the
questions will be simple enough for Quality Circles.
IX MY CURRENT EFFORTS
In fall 2006 the freshmen in engineering at SDSM&T were
introduced to the Ishikawa diagram and asked the prepare
Ishikawa diagrams and check sheets. So, there is some
verification that the work can be done. Additionally, many
diagrams and check sheet are available for model fitting and
review. Some simple models have been fit to the data.
Experience has been gained in teaching the procedure.
In summer 2007 high school freshman in a program at
SDSM&T were introduced to the Ishikawa diagram in a manner
similar to those at students in the fall 2006 program.
The senior simulation class at SDSM&T this spring evaluated
their instructor using EIPI.
For a project in Technology Management at SDSM&T, Andreas
Eikeland prepared a set of fictional examples of use of EIPI in
four settings: education, metal processing, ship manufacturing,
and project planning.
A colleague at SDSM&T included an extended Ishikawa
procedure as an activity in an engineering education proposal.
The proposal was well reviewed by not funded.
XI SUMMARY
The hybrid procedures are called Extended Ishikawa – Pareto
Inspired (EIPI) procedures. Hopefully, the double rhyming
acronym will be memorable and fun. A few people have
mentioned that they are tempted to break into song upon hearing
it.
The current status of the Ishikawa diagram was described. A
method for extending its use when sampling or multi-site
situations require new practices was introduced. Since much of
the work exploits basic Quality Circle tools, much of the work
can be done at a Quality Circle level. Because the solution
involves their use references for capture-recapture methods are
given. Some simple but crude statistical methods to facilitate
sampling were given. The follow up procedure also exploits
another basic Quality Circle tool, and leads to a hybrid
procedure with the acronym, EIPI. Recent activities with regard
to EIPI are listed, also.
We have an evolutionary Quality concept: expanding the use of
Ishikawa diagrams by incorporating Quality Circle tools and
sampling. Researchers that can print their instruments may call
Much work could be done to improve EIPI methods and their
use. Obvious things such as developing new audiences and
trying Extended Ishikawa as a multi-site collaboration tool need
Figure 3 a generic Pareto Chart
to be done. Improvement of statistical theory and the related area
of exploiting existing software is a vast area of potential work.
Making the EIPI procedures accessible, and easier to use via the
world wide web may be an even larger area of potential work.
XII REFERENCES
Amstrup, S. C., McDonald, T. L., and Manly, B. F. J. (eds.)
(2005), Handbook of Capture-Recapture Analysis, Princeton
University Press, Princeton, NJ.
CARE-2 http://chao.stat.nthu.edu.tw/softwareCE.html
Dia http://live.gnome.org/Dia
Evans, D. L., Leemis, L. M., and Drew, J. H. (2006), “The
Distribution of Order Statistics for Discrete Random Variables
with Application to Bootstrapping,” INFORMS Journal on
Computing, 18, 19-30.
Ishikawa, K. (1986), Guide to Quality Control, Productivity
Incorporated
Juran, J. M. and Godfrey, A. B. (1998), Juran's Quality
Handbook, McGraw-Hill Professional, New York, NY.
Open Office http://www.openoffice.org/
MARK http://www.phidot.org/software/mark
Royle, J. A., Dorazio R. M. , and Link, W. A.(2007), “Analysis
of Multinomial Models With Unknown Index Using Data
Augmentation,” Journal of Computational and Graphical
Statistics, 16, 67-85.
Summers, D.C.S. (2007), Six Sigma: Basic Tools and
Techniques, Prentice Hall, New York, NY.
Swanson, R. C. (1995), The Quality Improvement Handbook, St.
Lucie Press, Delray Beach, Florida.
Visio http://office.microsoft.com/en-us/visio/default.aspx
WinBUGS
http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml
Word www.Office2007.com